(see [1]}) shows that the condition (a) of Lemma 1 is satisfied for \((X,m)=(\mathbb {D},dA)\)  and \((\Omega ,\mu )=(\mathbb {D},\mu )\) . Conditions (b) and (c) are
the consequences of the inequality
\(\Vert f\circ \varphi _w\Vert _{H^p}\le \left(\frac{1+|w|}{1-|w|}\right)^{1/p} \Vert f\Vert _{H^p}.\) 
